We have little direct evidence of what Galileo’s feelings were about his experiments because, unlike Darwin, he has left us no autobiography, nor, as in the case of Newton, a hoard of secret documents recording his inmost thoughts only to be discovered three centuries later. The one thing we can be sure of is that he did not think of them as if he were living in the twenty first century, even though that is what many people seem to think. What he has left us, among less important works, are two dialogues presenting his ideas in dramatic form, The Dialogue of the Two Greatest Systems of the World and, the mature work of his old age, The Discourses on Two New Sciences. In each case he presents his material in the form of a lively conversation between three protagonists, Salviati who broadly speaking represents Galileo’s own point of view, a sensible and cultivated acquaintance called Sagredo who was in fact a close friend of Galileo, and a fall guy, Simplicio, who unfailingly and simplistically puts forward the Aristotelian point of view. In fact, it is not unlikely that a major reason why Galileo was called to trial by the Inquisition was because the paranoid Urban VIII suspected that Simplicio was meant to be a satirical portrait of himself. For such trivial reasons do the great watersheds of history so often come about. We also know that he was a great lover of music. He was an accomplished player of the lute and it is perhaps not without significance, as will be seen, that the lute was a fretted instrument.
Music was intrinsic to his experimentation. In a fascinating article in Scientific American for 1975 Stillman Drake suggested that Galileo used music to make his crucial free fall experiments. To perform them he had to have a measure of time that was accurate to much less than a second. But there were no clocks or metronomes in Galileo’s time that could reliably measure time even to a second, let alone less. That was why Galileo used his own pulse to measure the swing of a pendulum. Stillman Drake points out that the conductor of an orchestra divides time into equal intervals with his baton without even thinking of minutes or seconds. He keeps an even beat and divides that beat into smaller and smaller intervals that last for far less than a second with extraordinary precision, and his tempo is read by the orchestra with equally astonishing accuracy. If an instrument comes in too early or too late by far less than a second the mistake and the disharmony are glaringly obvious, and we all quite unthinkingly perform just such amazing feats of perfect time keeping when we dance and sing.
In Galileo’s account of the crucial experiment in free fall whereby he showed that the distance of the fall is proportionate to the square of the time, he says that he did not divide equally the time taken but rolled his balls down a slight incline marked off in regular units of distance (did he get this idea from the fretting of his lute?). He rolled the ball down as far as one marker, he tells us, while water poured out of a container through a narrow orifice. He weighed the water. He then rolled the ball down as far as the second marker and weighed the water again. He thus discovered that the distances were in square to the weights of the water and therefore indirectly to the different lengths of time that the water took to pour through the hole. But in fact this method could not possibly have given him the answer he needed because the tiny fractions of difference required could hardly have been registered by a seventeenth century weighing machine. Through experiments of his own, Drake showed that performing the experiment while singing the same song and stopping singing at the precise point when the ball reaches the appointed marker gives an entirely satisfactory result, so, given his interest in music, there is a strong case that this is the method Galileo must have used.
He also performed a number of less well known experiments on music directly. In one experiment, which both Salviati and Sagredo claimed to have done, a glass almost filled with water is made to give a musical note by running the finger round the rim. This sets up a pattern of waves in the water. Galileo claims that when the finger is moved faster to the point that the note is an octave higher ‘there will appear other smaller waves, which with infinite precision cut in half the first ones’. D.P. Walker comments that since it would be almost impossible to observe what the waves were doing ‘with infinite precision’ this was most likely a thought experiment which was never actually carried out. A second experiment he says he came upon by chance. He was scraping a brass plate when he noticed that sometimes when he moved the chisel rapidly he heard a whistling sound, ‘un sibilo molto gagliardo e chiaro’. When this happened the chisel left a pattern of equidistant lines on the brass. He also noticed in the hand holding the chisel a trembling like that felt in the larynx when one voices a word as opposed to whispering it. He then succeeded in making a noise with the chisel that was a fifth higher than the first one by moving the chisel faster. Whereas there were thirty striated lines in the first instance there were forty-five in the second, the same ratio of 3:2 that is found in the musical fifth. He had shown, or thought he had shown, that distance is related to pitch, the underlying logic of sound waves.
Again Walker thinks that this must have been a thought experiment about which he had not thought enough, as opposed to one that he had actually done. If he moved the chisel faster in the second case, as he says he did, then he would have covered the distance in less time in the second instance than in the first, and the chisel would have made fewer strokes than forty-five. I’m not sure that Walker is right about this. The whole point, I thought, was that at the higher note the chisel was also making its marks faster at a greater rate of vibration. Actually, my head is spinning trying to think about this so I’m not quite sure what I’m saying. In any case, of course, since the times taken were different, because in the second case he was moving the chisel faster, the comparison would have been invalid, so perhaps Walker is right after all. Galileo did not, at any rate, establish that the ratio of forty-five chisel strokes to thirty corresponds to the sound interval of a fifth. What, however, was implicit in Galileo’s musical experiments is that when two strings are played, the sweetness or consonance of the sound is determined by the degree to which the pulses of the sound waves set up co-incide. This, of course, is exactly the same logic that led Thomas Young to the wave theory of light. In the octave every second pulse co-incides, in a fifth every third one and in a fourth every fifth one. The ear hears other chords as discordant because the sound waves are co-inciding less frequently. These observations were known already and were not original to Galileo. But what was new was the conclusion he drew from it, reasoning that it is because of this lesser co-inciding that the supposedly harsher discords are more pleasing to the ear, not less pleasing as you might think, than the more obviously concordant ones. The octave is insipid because the pulses produce a boring rhythm. They coincide too often. In the less regular cases the less frequent co-incidence ‘makes such a tickling and stimulation of the cartilage of the ear-drum that, tempering the sweetness with a dash of sharpness, it seems delightfully to kiss and bite at the same time (fa una titillazione ed un sollecito tale sopra la cartalgione del timpano, che temperando la dolcezza con una sprezza d’acrimonia, par che insieme soavemente baci e morda)’. Thirds and sixths actually make music more harmonious. We know it when we hear polyphony and now we know why because science explains it .He was, indeed, his father’s son.